In many shell analyses, the shell is constructed of layers of different
materials and it is important to include thermal effects. If the temperature variations, or the temperature gradients are large, significant deformations can occur, together with a very complex shell behavior.

ADINA is a powerful tool to solve such problems. Here we present a coupled nonlinear thermo-mechanical analysis
of a composite shell structure. The cylindrical composite shell, simply supported around its edges, is made up of four material layers, two orthotropic elastic materials as the core and two isotropic elastic-plastic materials on the top and bottom. The environmental temperatures inside and outside of the shell are raised.

This temperature loading leads to a gradual increase in temperature and temperature gradient in the shell, mainly by surface convection, causing thermal expansion. The external temperatures are then returned to their initial levels, that is, the shell cools down to its initial temperature state.

Despite the simple shell geometry, the response is highly nonlinear, see movie above and Figures
below. The composite shell tries to expand uniformly, but the
deformation patterns change due to buckling, as well as plastic deformations. Buckling occurs at a shell mid-surface temperature rise of about 140°C. Also, reverse plastic deformations take place during unloading. The load deflection curve at point A in the shell is shown in Fig. 1, and the effective plastic strain on the top surface
of the shell after the temperature returns to its initial state is shown in Fig. 2.

Figure 1 Load deflection curve at point A in the shell

Figure 2 Effective plastic strain in the shell top surface after shell
temperature returns to initial state

A solution is available in the academic literature for a simpler model, where all four composite layers are elastic orthotropic, the temperature is everywhere in the structure
prescribed, and the geometry is slightly different (see Ref.). As the prescribed temperature increases, the elastic composite shell experiences a similar buckling behavior to that seen in the above
analysis. The solution given in the reference compares well with an
ADINA solution as shown in Fig. 3.

Figure 3 Comparison of solution of Ref. with solution using
ADINA

These analyses illustrate that ADINA can be used efficiently for thermo-mechanical solutions of shell structures.